A Census of Eddy Activities in the South China Sea During 1993-2007

Numerous mesoscale eddies occur each year in the South China Sea (SCS), but their statistical characteristics are still not well documented. A Pacific basin-wide three dimensional physical-biogeochemical model has been developed and the result in the SCS subdomain is used to quantify the eddy activities during the period of 1993-2007. The modeled results are compared with a merged and gridded satellite product of sea level anomaly by using the same eddy identification and tracking method. On average, there are about 32.9 +/- 2.4 eddies predicted by the model and 32.8 +/- 3.4 eddies observed by satellite each year, and about 52% of them are cyclonic eddies. The radius of these eddies ranges from about 46.5 to 223.5 km, with a mean value of 87.4 km. More than 70% of the eddies have a radius smaller than 100 km. The mean area covered by these eddies each year is around 160,170 km(2), equivalent to 9.8% of the SCS area with water depths greater than 1000 m. Linear relationships are found between eddy lifetime and eddy magnitude and between eddy vertical extent and eddy magnitude, showing that strong eddies usually last longer and penetrate deeper than weak ones. Interannual variations in eddy numbers and the total eddy-occupied area indicate that eddy activities in the SCS do not directly correspond to the El Nino-Southern Oscillation events. The wind stress curls are thought to be an important but not the only mechanism of eddy genesis in the SCS.

A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.